1. Field of Invention
The present disclosure relates generally to a system and a method for de-saturating a control moment gyroscope used for applying a control moment to an aircraft or other vehicle. More specifically, the present disclosure relates to a system and method of de-saturating a control moment gyroscope that leverages an aerodynamic moment created when the aircraft is subjected to a flow angle.
2. Description of Prior Art
Control moment gyroscopes (CMG) are typically used for controlling attitude of spacecraft. Using a CMG, a torque can be generated within and imparted onto the spacecraft via an exchange of angular momentum. A CMG may be defined as a way to exchange angular momentum from a flywheel spinning at a constant rate, that is converted to torque by pivoting or gimballing the flywheel about an axis transverse to the spinning flywheel, that then is applied to the vehicle of interest via rigid mounting of the CMG system to the structure of the vehicle. The output torque of the CMG typically orients orthogonal to both the flywheel axis and the gimbal axis by gyroscopic precession. As an example, a prior art CMG assembly is shown in a side perspective view in FIG. 1. The CMG assembly 10 includes a rotating flywheel 12 mounted coaxially about an axis 14. The axis 14 is secured within a U-shaped yoke 16 having a lower frame portion set apart from the outer diameter of the flywheel 12. Attached on an end of the yoke 16 is a flywheel motor 18 that is coupled to the axle 14; operating the motor 18 rotates the axle 14 for delivering rotational motion to the flywheel 12.
A torque T may be generated by first spinning the flywheel 12 and then pivoting the flywheel 12 about an axis transverse to the axle 14. A gimbal motor 20 with attached gimbal shaft 22 is shown for pivoting the yoke 16 and flywheel 12. Rotating the flywheel 12 shown at an angular velocity of ωf, generates an angular momentum vector L. In the example of FIG. 1, the angular momentum vector L is equal to the moment of inertia (I) of the rotating flywheel 12 multiplied by the angular velocity ωf of the flywheel 12. Pivoting the flywheel 12 by rotating the shaft 22, at a gimbal rate represented by the angular velocity ωg, changing the gimbal angle φg of the shaft 22, produces a torque T: where the magnitude of torque T may be represented by (I)(ωg)(ωf). The torque T is oriented orthogonal to the axis Ax of the flywheel 12. The direction of the torque T remains orthogonal to the axis Ax, and therefore changes orientation as the flywheel 12 is pivoted by the gimbal motor 20.
FIG. 2 schematically illustrates a prior art “scissor pair” of CMG assemblies 10 shown oppositely oriented and anchored within an aircraft 24. The scissor pair CMG generate a pure output torque about the yaw or Z-body axis, as in the example shown in FIG. 2. In this arrangement, the flywheels 12 of the CMG assemblies 10 are aligned so that when in a neutral position the flywheels 12 and their angular momentum vectors are substantially coaxial but cancel one another. As the aircraft maneuvers and/or the gimbal angles of the individual CMG assemblies become non-zero, each assembly will generate torques about the X and Y aircraft body axes. However, since the flywheels 12 for each CMG assembly 10 are positioned such that their angular momentum vectors face in opposite directions, these undesired off-axis torques cancel one another so long as the gimbal angles and rates of each individual assembly are of equal magnitude. Thus, when the scissor pair CMG assemblies are pivoted at the same gimbal rate, but in opposite angular directions, each CMG assembly 10 generates additive torque components along the Z-axis: where φg is defined as zero in the starting point shown in FIG. 2; both flywheel momentum vectors, L, lie in x-y plane at φg equal to zero.
The output torque in the z-direction, Tz, from the scissor pair assembly is a function of the cosine of the commanded gimbal angle φg;Tz=(I)(ωg)(ωf)cos(φg). For the purposes of discussion herein, a neutral position for the flywheel 12 is an initial orientation with φg=0. As such, the CMG assemblies 10 of FIG. 2 “saturate” after 90° of pivot from the neutral position and will no longer impart a torque along the Z-axis. Therefore, the CMG assemblies can be de-saturated by commanding the gimbal angles back towards neutral. Gimbal de-saturation commands will generate additional output torque on the vehicle that is undesired and requires balancing by an external torque on the vehicle such that the gimbal angles can be commanded towards neutral with no resultant dynamic response on the vehicle.